Why should you base your choice of what compound is the limiting reactant on its number of initial moles, not on its initial mass in grams?

A balanced chem. equation is based on moles NOT grams. EX --- 2H2 + O2 --> 2H2O ... means 2 moles of H2 combine with 1 mole O2, NOT that 2 grams H2 combine with 1 gram O2.

Well, looking at the microscopic scale, mass doesn't really matter when talking about one molecule reacting with two other molecules, for example. It's really the ratios of amounts of each molecule that matters because the molecules could have very different masses. Like David mentioned, it's why we use amount or moles to represent the coefficients of a chemical equation, not mass.